2(4h^2+6h-612)=0

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Solution for 2(4h^2+6h-612)=0 equation: 


Simplifying
2(4h2 + 6h + -612) = 0

Reorder the terms:
2(-612 + 6h + 4h2) = 0
(-612 * 2 + 6h * 2 + 4h2 * 2) = 0
(-1224 + 12h + 8h2) = 0

Solving
-1224 + 12h + 8h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-306 + 3h + 2h2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-306 + 3h + 2h2)' equal to zero and attempt to solve:

Simplifying
-306 + 3h + 2h2 = 0

Solving
-306 + 3h + 2h2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-153 + 1.5h + h2 = 0

Move the constant term to the right:

Add '153' to each side of the equation.
-153 + 1.5h + 153 + h2 = 0 + 153

Reorder the terms:
-153 + 153 + 1.5h + h2 = 0 + 153

Combine like terms: -153 + 153 = 0
0 + 1.5h + h2 = 0 + 153
1.5h + h2 = 0 + 153

Combine like terms: 0 + 153 = 153
1.5h + h2 = 153

The h term is 1.5h.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5h + 0.5625 + h2 = 153 + 0.5625

Reorder the terms:
0.5625 + 1.5h + h2 = 153 + 0.5625

Combine like terms: 153 + 0.5625 = 153.5625
0.5625 + 1.5h + h2 = 153.5625

Factor a perfect square on the left side:
(h + 0.75)(h + 0.75) = 153.5625

Calculate the square root of the right side: 12.392033731

Break this problem into two subproblems by setting 
(h + 0.75) equal to 12.392033731 and -12.392033731.


Subproblem 1
h + 0.75 = 12.392033731

Simplifying
h + 0.75 = 12.392033731

Reorder the terms:
0.75 + h = 12.392033731

Solving
0.75 + h = 12.392033731

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + h = 12.392033731 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + h = 12.392033731 + -0.75
h = 12.392033731 + -0.75

Combine like terms: 12.392033731 + -0.75 = 11.642033731
h = 11.642033731

Simplifying
h = 11.642033731


Subproblem 2
h + 0.75 = -12.392033731

Simplifying
h + 0.75 = -12.392033731

Reorder the terms:
0.75 + h = -12.392033731

Solving
0.75 + h = -12.392033731

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + h = -12.392033731 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + h = -12.392033731 + -0.75
h = -12.392033731 + -0.75

Combine like terms: -12.392033731 + -0.75 = -13.142033731
h = -13.142033731

Simplifying
h = -13.142033731


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {11.642033731, -13.142033731}
Solution
h = {11.642033731, -13.142033731}

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